Answer to Question #304335 in Finance for memo

Question

ABC and DEF are identical firms except that DEF is more levered. Both companies will remain in business for one more year. The companies’ economists agree that the probability of the continuation of the current expansion is 80 % for the next year, and the probability of a recession is 20 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $2.7 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $1.1 million. ABC’s debt obligation requires the firm to pay $0.9 million at the end of the year. DEF’s debt obligation requires the firm to pay $1.2 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 15 percent. 

a. What is the value today of ABC’s debt and equity? What about that for DEF’s? 

b.  DEF’s CEO recently worried that its firm value should be lower than ABC’s because the firm has more debt and therefore more bankruptcy risk. Do you agree or disagree with this statement?   

Answer 1

ABC

For expansion:

Earnings available to equity holder = EBIT - debt obligation

=$2,700,000 - $900,000

=$1,800,000

 

For recession:

Earnings available to equity holder = EBIT - debt obligation

=$1,100,000 - $900,000

=$200,000

 

Debt's market value = (expansions' debt obligation * probability percentage of expansion + recessions' debt obligation * probability percentage of recession) / (1+discount rate)

=$\frac{(\$900,000 \times 0.70 + \$900,000 \times0.30) }{ (1 + 0.13)}$

=$\frac{(\$630,000 + \$270,000) }{ 1.13}$

=$7,96,460.18

 

Equity market value = (expansions of Earnings available to equity holder * probability percentage of expansion + recessions of Earnings available to equity holder * probability percentage of recession) / (1+discount rate)

=$\frac{(\$1,800,000 \times0.70 + \$2,000,000 \times0.30)}{(1 + 0.13)}$

=$\frac{(\$1,260,000 + \$600,000)}{1.13}$

=$\frac{\$1,860,000}{1.13}$

=$1,646,017.70

 

DEF 

For expansion:

Earnings available to equity holder = EBIT - debt obligation

=$2,700,000 - $1,200,000

=$1,500,000

 

For recession:

Earnings available to equity holder = EBIT - debt obligation

=$1,100,000 - $1,200,000

=$0

 

Debt's market value = (expansions' DEF debt obligation * probability percentage of expansion + recessions' debt obligation * probability percentage of recession) / (1+discount rate)

$=\frac{(\$1,200,000\times× 0.70 + \$1,200,000 \times0.30)}{(1 + 0.13)}$

=$\frac{(\$840,000 + \$360,000) }{1.13}$

=$\frac{\$1,200,000}{1.13}$

=$1061946.90

 

Equity market value = (expansions of Earnings available to equity holder * probability percentage of expansion + recessions of Earnings available to equity holder * probability percentage of recession) / (1+discount rate)

=$\frac{(\$1,500,000 \times 0.70 + \$\times0.30)}{ (1 + 0.13)}$

=$\frac{\$840,000 + \$360,000}{1.13}$

=$929203.54

 

Total value = Equity market value + Debt's market value

ABC= $16,46,017.70 + $7,96,460.18

=$24,42,477.88

DEF = $929203.54 + $1061946.90

=$19,91,150.44

Yes agree with this statement because the value of the both DEF is lower than ABC.